Liquid oxygen is stored in a thin$-$walled, spherical container $0\mathrm{.}8$ m in diameter, which is enclosed within a second thin$-$walled, spherical container $1\mathrm{.}2$ m in diameter. There is a tiny hole given at the topmost point of the container for safety purposes. The opaque, diffuse, gray container surfaces have an emissivity of $0\mathrm{.}5$ and are separated by an evacuated space. The outer surface is at $300$ K and the inner surface is at $90$ K$.$ Take the latent heat of vaporization of oxygen $($hlg$)$ is $2\mathrm{.}13105$ J$/$kg$.($a$)$ What is the steady mass rate of oxygen lost due to evaporation? $($b$)$ To reduce the mass rate obtained in part $($a$),$ it is proposed to reduce the emissivity of container surfaces by polishing or coating. If the emissivity is reduced to $0\mathrm{.}1,$ recalculate the steady mass rate of oxygen lost due to evaporation. Does the proposal serve the purpose? $($c$)$ To reduce the mass rate obtained in part $($a$),$ it is also proposed that a thin radiation shield of $1$ m diameter and $3=0\mathrm{.}05($both sides$)$ can be inserted midway between the inner and outer surfaces. Calculate the steady mass rate of oxygen lost due to evaporation for this case. Does the proposal also serve the purpose?